This section is optional; only the last two sections of Chapter Five require this material.

We have described the projection from into its plane subspace as a "shadow map". This shows why, but it also shows that some shadows fall upward.

So perhaps a better description is: the projection of is the in the plane with the property that someone standing on and looking straight up or down sees . In this section we will generalize this to other projections, both orthogonal (i.e., "straight up and down") and nonorthogonal.